Given that the directrix is at y = 4 and the focus is at (0, -4), then the vertex is at (h, k) = (0, 0).
p is the distance between the vertex and the focus and between the vertex and the directrix = 4 and since the focus is below the directrix, p is negative, i.e. p = -4
Equation of a parabola is given by (x - h)^2 = 4p(y - k)
Therefore, the required equation is (x - 0)^2 = 4(-4)(y - 0)
x^2 = -16y
y = -1/16 x^2
Answer:
[11 2]
Step-by-step explanation:
10 to -1 is 11 and-3 to -5 is 2 therfore you have the distance of 11 and 2
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Square Rug
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Area = Length x Length
Area = 6.3 x 6.3
Area = 39.69 ft²
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Rectangle Rug
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Area = Length x Width
Area = 4.8 x 8.2
Area = 39.36 ft²
39.69 ft² is bigger than 29.36 ft², so the square rug is bigger.
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Ans: The Square Rug covers a greater area
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<span>The area of the base is x^2> The height is h. Each side of the box has area xh. There are 4 sides of the box so the total surface area of the box is x^2+4xh and that is equal to 1000. Solve that equation for h:
x^2+4xh = 1000 h = (1000-x^2)/4x so the Volume = x^2[(1000-x^2)/4x]
Simplify and get V = 250x-x^3/4
The volume will be a maximum when its first derivative is 0.
V' = 250-3/4x^2
Set to 0 and solve. x=18.26
Now plug into the volume function to find the maximum volume:
V=250(18.26)-(18.26)^3/4
V= 4564.35 - 1522.10 =3042.25</span>
